Question

Яка з точок М(0;3;0), Р(1;0;1) ,С(0;0;2) К(-3;0;0),А(3;0;4), належить осі аплікат?

Answer 1

Відповідь: точка С(0;0;2)

Answer 2

Definition of an Aplikat

An aplikat, also known as an axis of a line, is a straight line that passes through two points in space. It is used to determine the direction and orientation of a line. In this case, we are given five points: M(0, 3, 0), R(1, 0, 1), S(0, 0, 2), K(-3, 0, 0), and A(3, 0, 4). We need to determine if there is an aplikat that passes through these points.

Determining if an Aplikat Exists

To determine if an aplikat exists that passes through these points, we can use the equation of a line in three-dimensional space. The equation of a line passing through two points (x1, y1, z1) and (x2, y2, z2) is given by:

(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) = (z - z1) / (z2 - z1)

We can choose any two points from the given points and substitute their coordinates into the equation to check if the other points satisfy the equation as well.

Let's choose points M(0, 3, 0) and R(1, 0, 1) to form the equation:

(x - 0) / (1 - 0) = (y - 3) / (0 - 3) = (z - 0) / (1 - 0)

Simplifying the equation, we get:

x = 0 y = 3 - 3z z = z

Now, let's substitute the coordinates of the other points into the equation to check if they satisfy it.

For point S(0, 0, 2):

0 = 0 0 = 3 - 3(2) 2 = 2

The coordinates of point S satisfy the equation.

For point K(-3, 0, 0):

-3 = 0 0 = 3 - 3(0) 0 = 0

The coordinates of point K satisfy the equation.

For point A(3, 0, 4):

3 = 0 0 = 3 - 3(4) 4 = 4

The coordinates of point A satisfy the equation.

Since all the given points satisfy the equation, we can conclude that there is an aplikat that passes through the points M(0, 3, 0), R(1, 0, 1), S(0, 0, 2), K(-3, 0, 0), and A(3, 0, 4).

Therefore, an aplikat passes through the points M(0, 3, 0), R(1, 0, 1), S(0, 0, 2), K(-3, 0, 0), and A(3, 0, 4).